An organization that advises several union pension funds invested in Rupert Murdoch’s 21st Century Fox called on Thursday for the company to overhaul its board and conduct a comprehensive review of its workplace culture in the wake of sexual and racial harassment scandals at its Fox News division.

The organization, CtW Investment Group, sent a letter to Viet D. Dinh, the chairman of the board’s nominating and corporate governance committee, accusing directors of failing to effectively address a “longtime ethics crisis” at Fox News, and risking the company’s reputation, operations and long-term value.

“If the board was aware of the settlements and refused to investigate and mitigate the risk, instead allowing the problem to fester, then it failed in its risk oversight function and facilitated a tone at the top that permits unethical behavior by high performers,” Dieter Waizenegger, CtW’s executive director, wrote in the letter, referring to settlements paid to women at Fox News who made sexual harassment allegations.

“If the information of the settlements did not reach the board,” Mr. Waizenegger added, “then it failed to ensure that the proper corporate controls were in place.”

In a statement, 21st Century Fox said, “We take seriously all communications from shareholders and investment groups, and will respond accordingly.”

The move is one of the investment community’s harshest public critiques of 21st Century Fox over its handling of the scandal at Fox News. The company has been dealing for more than a year with the fallout from a crisis that exposed a workplace that women said was rife with harassment and where they feared reporting inappropriate behavior. The scandal led to the departure of Roger E. Ailes, the founding chairman of Fox News; Bill O’Reilly, the former Fox News host; and several others.

Even as 21st Century Fox tries to move on, the United States attorney’s office in Manhattan is conducting a criminal investigation into Fox News’s handling of the sexual harassment complaints. The company also faces continuing regulatory scrutiny in Britain over its $15 billion bid to acquire full control of Sky, the European satellite giant.

The financial price of the scandal has mounted, with 21st Century Fox incurring about $50 million in costs tied to the settlement of sexual harassment and discrimination allegations involving Fox News in the year that ended June 30. That figure does not include a $40 million payout to Mr. Ailes or a $25 million payout to Mr. O’Reilly. And, according to CtW, 21st Century Fox could face penalties of $140 million if the Sky deal is delayed into 2018 and $164 million if it falls through altogether.

The company said in a proxy statement filed with the Securities and Exchange Commission last month that it had “made significant changes to the leadership and management of Fox News Channel after allegations of misconduct at the Fox News Channel business.” It also said it had hired a new global head of human resources at 21st Century Fox and a new head of human resources at Fox News. And, the company said, nearly 7,000 employees had received training about workplace behavior in the past 12 months.

In addition, 21st Century Fox said it had approved the creation of a new “compliance steering committee” to be made up of company executives and answerable to the board.

CtW said in its letter that the changes were inadequate and that 21st Century Fox needed to commit to making corporate governance changes in order for the organization to support the re-election of the board’s audit committee members at the company’s annual shareholder meeting next month.

“We need not wait on the results of any U.S. attorney’s office’s investigation into what the board did or did not know regarding the settlements to conclude that the board failed,” Mr. Waizenegger said in the letter.

CtW called specifically for the resignation of Roderick Eddington, the company’s lead director and the chairman of the audit committee, saying that he “clearly failed in his risk oversight responsibilities.” The group is also urging that 21st Century Fox appoint two new directors with backgrounds in human resources, expand the number of independent directors and increase the number of women on the board. (The company board now has one female director.)

In addition, CtW said 21st Century Fox should create a new committee composed of independent directors focused on “organizational culture, workplace safety and health, work force diversity and pay equality, and employee engagement and development.”

Charles M. Elson, director of the John L. Weinberg Center for Corporate Governance at the University of Delaware, said the scandal at Fox News had raised concerns about management and board oversight of the parent company.

The broader corporate governance issue at 21st Century Fox, Professor Elson said, was the company’s dual-class share structure, which gives voting rights to the owners of one class of stock but not to the other. The Murdoch family controls about 40 percent of the voting stock in the company, giving it significant sway over the board.

“The question is, if the independent directors had known, could they have done anything?” Professor Elson said.

Shareholders are expected to vote at the company’s annual meeting on a proposal from the Nathan Cummings Foundation that would end the dual-class share structure in favor of giving each share of common stock one vote.

The foundation made a similar proposal with regard to 21st Century Fox’s share structure in the past, and the allegations of sexual harassment and racial discrimination at Fox News have revived the focus on the company, said Laura Campos, the foundation’s director of corporate and political accountability.

“For us, that is underpinning many of the problems the company has faced,” Ms. Campos said of the dual-class structure.

The 21st Century Fox board has recommended that shareholders reject the proposal, stating that “the current dual-class capital structure continues to be appropriate and is in the best interest of the company and its stockholders."

The calls for corporate governance reform at 21st Century Fox echo a push by shareholders for the Murdoch media empire to make changes six years ago after a phone-hacking scandal in Britain prompted investor concern.

A version of this article appears in print on , on Page B3 of the New York edition with the headline: Investor Presses for Change To 21st Century Fox Board. Order Reprints | Today’s Paper | Subscribe